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Beta decays as sensitive probes of lepton flavor universality

Nuclear $β$ decays as well as the decay of the neutron are well-established low-energy probes of physics beyond the Standard Model (SM). In particular, with the axial-vector coupling of the nucleon $g_A$ determined from lattice QCD, the comparison between experiment and SM prediction is commonly used to derive constraints on right-handed currents. Further, in addition to the CKM element $V_{us}$ from kaon decays, $V_{ud}$ from $β$ decays is a critical input for the test of CKM unitarity. Here, we point out that the available information on $β$ decays can be re-interpreted as a stringent test of lepton flavor universality (LFU). In fact, we find that the ratio of $V_{us}$ from kaon decays over $V_{us}$ from $β$ decays (assuming CKM unitarity) is extremely sensitive to LFU violation (LFUV) in $W$-$μ$-$ν$ couplings thanks to a CKM enhancement by $(V_{ud}/V_{us})^2\sim 20$. From this perspective, recent hints for the violation of CKM unitarity can be viewed as further evidence for LFUV, fitting into the existing picture exhibited by semi-leptonic $B$ decays and the anomalous magnetic moments of muon and electron. Finally, we comment on the future sensitivity that can be reached with this LFU violating observable and discuss complementary probes of LFU that may reach a similar level of precision, such as $Γ(π\toμν)/Γ(π\to eν)$ at the PEN and PiENu experiments or even direct measurements of $W\toμν$ at an FCC-ee.